Related papers: Stochastic reaction networks within interacting co…
The notion of entropy is shared between statistics and thermodynamics, and is fundamental to both disciplines. This makes statistical problems particularly suitable for reaction network implementations. In this paper we show how to perform…
We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…
Reaction networks have been widely used as generic models in diverse areas of applied sciences, such as biology, chemistry, ecology, epidemiology, and computer science. A reaction network incorporating noisy effects is modeled as a…
Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…
We consider stochastic reaction-diffusion equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given supplemented by a…
We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are…
The seemingly stochastic transient dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference. In vitro neurons, on the other hand, exhibit a highly deterministic…
Reaction networks have become a major modelling framework in the biological sciences from epidemiology and population biology to genetics and cellular biology. In recent years, much progress has been made on stochastic reaction networks…
Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…
We consider the important problem of estimating parameter sensitivities for stochastic models of reaction networks that describe the dynamics as a continuous-time Markov process over a discrete lattice. These sensitivity values are useful…
Simplified stochastic models are widely used in the study of frequency-resolved noise propagation in biochemical reaction networks, a common measure being the coherence between random fluctuations in molecule number trajectories. Such…
The stochastic reaction network in which chemical species evolve through a set of reactions is widely used to model stochastic processes in physics, chemistry and biology. To characterize the evolving joint probability distribution in the…
Single-cell data reveal the presence of biological stochasticity between cells of identical genome and environment, in particular highlighting the transcriptional bursting phenomenon. To account for this property, gene expression may be…
Mathematical models are an important tool for neuroscientists. During the last thirty years many papers have appeared on single neuron description and specifically on stochastic Integrate and Fire models. Analytical results have been proved…
Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often…
We investigate to what extent the interaction dynamics of a population of wild house mouse (Mus musculus domesticus) in their environment can be explained by a simple stochastic model. We use a Markov chain model to describe the transitions…
Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by…
The past few decades have seen robust research on questions regarding the existence, form, and properties of stationary distributions of stochastically modeled reaction networks. When a stochastic model admits a stationary distribution an…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…